Gauge-free Hamiltonian structure of the spin Maxwell–Vlasov equations

We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized plasma systems. We find that it is possible to construct a generalized noncanonical Poisson bracket on the extended phase space, and discuss the implications of our findings, including stability of monotonic equilibria.

► A spin-Maxwell–Vlasov kinetic theory with intrinsic spin is described.
► The gauge-free Hamiltonian structure with noncanonical Lie–Poisson bracket is obtained.
► Implications of our findings, including stability of monotonic equilibria, are described.